Question

A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in the figure, indicate the one that represents the velocity $\left(v\right)$ of the pebble as a function of time $\left(t\right)$.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

When the pebble is falling through the viscous oil, the viscous force (drag force) acting on pebble is,
$F=6\pi r\eta v$
The direction of viscous force $\left(F_v\right)$ and buoyant force ($F_b$) will be opposite to that of velocity.
However, weight of the body acting downwards, tends to accelerate the body. Initially $W>F_v+F_b$, hence the pebble will accelerate.

With increase in $v$, $F_v$ increases. This diminishes the acceleration of the pebble.
At some instant, $W=F_v+F_b$ and net force on pebble $F_{\text{net}}=0$
$\Rightarrow a=0$

Thereafter, the pebble will continue to move at constant velocity $v=v_T$, called terminal velocity.

As the force is variable, hence acceleration is also variable, so $v-t$ graph will not be a straight line. Velocity increases first and then become constant.
$\therefore$ Option $\left(c\right)$ is correct.